It aint about trying to get her mom to like you. If her mom is really physically abusive towards her then it needs to be reported. If she really has burned her with cigarettes and cut her as you say then there will be marks that can be shown, and it will only take one single phone call to get her out of that situation.
99% of normal 16 year old girls are not ready for that level of commitment. Someone who has been mentally and physically abused, and who has been suicidal ABSOLUTELY IS NOT ready for that level of commitment.
You don't even know who she will be when she is 18... neither does she.